A new looped-functional for stability analysis of sampled-data systems

Abstract In this paper, a new two-sided looped-functional is introduced for stability analysis of sampled-data systems. The functional fully utilizes the information on both the intervals x ( t ) to x ( t k ) and x ( t ) to x ( t k + 1 ) . Based on the two-sided functional, an improved stability condition is derived in the form of linear matrix inequality (LMI). Numerical examples show that the result computed by the presented condition approximates nearly the theoretical bound (bound obtained by eigenvalue analysis) and outperforms substantially others in the existing literature.

[1]  Corentin Briat,et al.  A looped-functional approach for robust stability analysis of linear impulsive systems , 2012, Syst. Control. Lett..

[2]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[3]  Corentin Briat,et al.  Convex Dwell-Time Characterizations for Uncertain Linear Impulsive Systems , 2012, IEEE Transactions on Automatic Control.

[4]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[5]  Y. Shu.  Stability and stabilization of nonuniform sampling systems. , 2008 .

[6]  Chung-Yao Kao,et al.  On Stability of Systems With Aperiodic Sampling Devices , 2013, IEEE Transactions on Automatic Control.

[7]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[8]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[9]  Alexandre Seuret,et al.  A novel stability analysis of linear systems under asynchronous samplings , 2012, Autom..

[10]  Corentin Briat,et al.  On the necessity of looped-functionals arising in the analysis of pseudo-periodic, sampled-data and hybrid systems , 2015, Int. J. Control.

[11]  Hisaya Fujioka,et al.  A Discrete-Time Approach to Stability Analysis of Systems With Aperiodic Sample-and-Hold Devices , 2009, IEEE Transactions on Automatic Control.

[12]  Kun Liu,et al.  Wirtinger's inequality and Lyapunov-based sampled-data stabilization , 2012, Autom..

[13]  Jin-Hua She,et al.  New results on stability analysis for systems with discrete distributed delay , 2015, Autom..

[14]  Chung-Yao Kao.  An IQC Approach to Robust Stability of Aperiodic Sampled-Data Systems , 2016, IEEE Transactions on Automatic Control.

[15]  Isabelle Queinnec,et al.  Regional Stability Analysis of Discrete-Time Dynamic Output Feedback Under Aperiodic Sampling and Input Saturation , 2016, IEEE Transactions on Automatic Control.

[16]  Corentin Briat,et al.  Stability analysis of uncertain sampled-data systems with incremental delay using looped-functionals , 2015, Autom..

[17]  João Pedro Hespanha,et al.  Exponential stability of impulsive systems with application to uncertain sampled-data systems , 2008, Syst. Control. Lett..

[18]  Young Soo Suh.  Stability and stabilization of nonuniform sampling systems , 2008, Autom..